Advanced Artificial Intelligence
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Part II. Statistical NLP
Advanced Artificial Intelligence
Probabilistic Logic Learning
Wolfram Burgard, Luc De Raedt, Bernhard Nebel, Lars Schmidt-Thieme
Many slides taken from Kristian Kersting and for Logic From Peter Flach’s Simply Logical
Overview
Expressive power of PCFGs, HMMs, BNs still limited• First order logic is more expressive
Why not combine logic with probabilities ?• Probabilistic logic learning
Short recap of logic (programs) Stochastic logic programs
• Extend PCFGs Bayesian logic programs
• Extend Bayesian Nets Logical HMMs
• Extend HMMs
ContextOne of the key open questions of artificial intelligence concerns
"probabilistic logic learning",
i.e. the integration of probabilistic reasoning with
machine learning.
first order logic representations and
Sometimes called Statistical Relational Learning
So far
We have largely been looking at probabilistic representations and ways of learning these from data• BNs, HMMs, PCFGs
Now, we are going to look at their expressive power, and make traditional probabilistic representations more expressive using logic • Probabilistic First Order Logics• Lift BNs, HMMs, PCFGs to more expressive
frameworks• Upgrade also the underlying algorithms
London Underground example
p.4
LRT Registered User No. 94/1954
BondStreet
GreenPark
OxfordCircus
PiccadillyCircus
CharingCross
LeicesterSquare
TottenhamCourt Road
JUBILEE BAKERLOO NORTHERN
CENTRAL
PICCADILLY
VICTORIA
UNDERGROUND
p.3
London Underground in Prolog (1) connected(bond_street,oxford_circus,central).
connected(oxford_circus,tottenham_court_road,central).connected(bond_street,green_park,jubilee).connected(green_park,charing_cross,jubilee).connected(green_park,piccadilly_circus,piccadilly).connected(piccadilly_circus,leicester_square,piccadilly).connected(green_park,oxford_circus,victoria).connected(oxford_circus,piccadilly_circus,bakerloo).connected(piccadilly_circus,charing_cross,bakerloo).connected(tottenham_court_road,leicester_square,northern).connected(leicester_square,charing_cross,northern).
Symmetric facts now shown !!!
p.3-4
London Underground in Prolog (2)Two stations are nearby if they are on the same line with at most one other station in between (symmetric facts not shown)
nearby(bond_street,oxford_circus).nearby(oxford_circus,tottenham_court_road).nearby(bond_street,tottenham_court_road).nearby(bond_street,green_park).nearby(green_park,charing_cross).nearby(bond_street,charing_cross).nearby(green_park,piccadilly_circus).
or betternearby(X,Y):-connected(X,Y,L).nearby(X,Y):-connected(X,Z,L),connected(Z,Y,L).
Facts: unconditional truthsRules/Clauses: conditional truthsBoth definitions are equivalent.
likes(peter,S):-student_of(S,peter).likes(peter,S):-student_of(S,peter).
“Peter likes anybody who is his student.”
clauseclause
atomsatoms
constantconstant variablevariable
termsterms
p.25
Clauses are universally quantified !!!:- denotes implication
p.8
Recursion (2)
A station is reachable from another if they are on the same line, or with one, two, … changes:
reachable(X,Y):-connected(X,Y,L).reachable(X,Y):-connected(X,Z,L1),connected(Z,Y,L2).reachable(X,Y):-connected(X,Z1,L1),connected(Z1,Z2,L2), connected(Z2,Y,L3).…
or betterreachable(X,Y):-connected(X,Y,L).reachable(X,Y):-connected(X,Z,L),reachable(Z,Y).
Substitutions
A substitution maps variables to terms: • {S->maria}
A substitution can be applied to a clause: • likes(peter,maria):-student_of(maria,peter).
The resulting clause is said to be an instance of the original clause, and a ground instance if it does not contain variables.
Each instance of a clause is among its logical consequences.
p.26
route
tottenham_court_road
leicester_square
route
noroute
p.12
Structured terms (2)
reachable(X,Y,noroute):-connected(X,Y,L).reachable(X,Y,route(Z,R)):-connected(X,Z,L), reachable(Z,Y,R).
?-reachable(oxford_circus,charing_cross,R).R = route(tottenham_court_road,route(leicester_square,noroute));R = route(piccadilly_circus,noroute);R = route(picadilly_circus,route(leicester_square,noroute))
functorfunctor
.
tottenham_court_road
leicester_square
.
[]
p.13-4
Lists (3)reachable(X,Y,[]):-connected(X,Y,L).reachable(X,Y,[Z|R]):-connected(X,Z,L), reachable(Z,Y,R).
?-reachable(oxford_circus,charing_cross,R).R = [tottenham_court_road,leicester_square];R = [piccadilly_circus];R = [picadilly_circus,leicester_square]
list functorlist functor
Answering queries (1)
Query:which station is nearby Tottenham Court Road?
?- nearby(tottenham_court_road, W).Prefix ?- means it‘s a query and not a fact.
Answer to query is: {W -> leicester_square}a so-called substitution.
When nearby defined by facts, substitution found by unification.
clauseclause
factfact
empty queryempty query
answer substitutionanswer substitution
substitutionsubstitution
queryquery
?-nearby(tottenham_court_road,W)
nearby(X1,Y1):-connected(X1,Y1,L1)
Fig.1.2, p.7
Proof tree
connected(tottenham_court_road,leicester_square,northern)
[]
{W->leicester_square, L1->northern}
?-connected(tottenham_court_road,W,L1)
{X1->tottenham_court_road, Y1->W}
Recall from AI course
Unification to unify two different terms Resolution inference rule Refutation proofs, which derive the
empty clause SLD-tree, which summarizes all
possible proofs (left to right) for a goal
:-teaches(peter,ai_techniques)
:-teaches(peter,expert_systems)
:-teaches(peter,computer_science)
?-student_of(S,peter)
SLD-tree: one path for each proof-tree
:-follows(S,C),teaches(peter,C):-follows(S,C),teaches(peter,C)
:-teaches(peter,expert_systems)
:-teaches(peter,computer_science) :-teaches(peter,ai_techniques)
?-student_of(S,peter)
student_of(X,T):-follows(X,C),teaches(T,C).follows(paul,computer_science).follows(paul,expert_systems).follows(maria,ai_techniques).teaches(adrian,expert_systems).teaches(peter,ai_techniques).teaches(peter,computer_science).
p.44-5
[][]
The least Herbrand model
Definition:• The set of all ground facts that are logically
entailed by the program All ground facts not in the LHM are false … LHM be computed as follows:
• M0 = {}; M1 = { true }; i:=0• while Mi =\= Mi+1 do
i := i +1; Mi := { h | h:- b1, …, bn is clause and there is a substitution such
that all bi Mi-1 }
• Mi contains all true facts, all others are false
Example LHM
KB: p(a,b). a(X,Y) :- p(X,Y). p(b,c). a(X,Y) :- p(X,Z), a(Z,Y).M0 = emtpy; M1 = { true }M2 = { true, p(a,b), p(b,c) }M3 = M2 U {a(a,b), a(b,c) }M4 = M3 U { a(a,c) }M5 = M4 ...
Stochastic Logic Programs
Recall :• Prob. Regular Grammars• Prob. Context-Free Grammars
What about Prob. Turing Machines ? Or Prob. Grammars ?• Stochastic logic programs combine
probabilistic reasoning in the style of PCFGs with the expressive power of a programming language.
Recall PCFGs
We defined
Stochastic Logic Programs
Correspondence between CFG - SLP• Symbols - Predicates• Rules - Clauses• Derivations - SLD-derivations/Proofs
So, • a stochastic logic program is an annotated logic
program. • Each clause has an associated probability label.
The sum of the probability labels for clauses defining a particular predicate is equal to 1.
An Example
:-card(a,s)
:-rank(a), suit(s)
:-suit(s)
[]
Prob derivation= 1 . 0.125 . 0.25
Example
s([the,turtle,sleeps],[]) ?
SLPs : Key Ideas
Example
Cards :• card(R,S) - no proof with R in {a,7,8,9…}
and S in { d,h,s,c} fails• For each card, there is a unique refutation• So,
Consider
same_suit(S,S) :- suit(S), suit(S).
In total 16 possible derivations, only 4 will succeed, so
Another example (due to Cussens)
Questions we can ask (and answer)about SLPs
Answers
The algorithmic answers to these questions, again extend those of PCFGs and HMMs, in particular,• Tabling is used (to record probabilities of partial
proofs and intermediate atoms)• Failure Adjusted EM (FAM) is used to solve
parameter re-estimation problem Additional hidden variables range over
• Possible refutations and derivations for observed atoms• Topic of recent research• Freiburg : learning from refutations (instead of atoms),
combined with structure learning
Sampling
PRGs, PCFGs, and SLPs can also be used for sampling sentences, ground atoms that follow from the program
Rather straightforward. Consider SLPs:• Probabilistically explore SLD-tree• At each step, select possible resolvents using the
probability labels attached to clauses • If derivation succeeds, return corresponding
(ground) atom• If derivation fails, then restart.
Bayesian Networks [Pearl 91]
Qualitative part:
Directed acyclic graph Nodes - random vars. Edges - direct influence
Compact representation of joint probability distributions
Quantitative part: Set of conditional probability distributions
0.9 0.1
e
b
e
0.2 0.8
0.01 0.99
0.9 0.1
be
b
b
e
BE P(A | B,E)Earthquake
JohnCalls
Alarm
MaryCalls
Burglary
P(E,B,A,M,J)
Together:Define a unique distribution in a compact, factored form
P(E,B,A,M,J)=P(E) * P(B) * P(A|E,B) * P(M|A) * P(J|A)
Traditional Approaches
P(j) = P(j|a) * P(m|a) * P(a|e,b) * P(e) * P(b)
+ P(j|a) * P(m|a) * P(a|e,b) * P(e) * P(b)
0.9 0.1
e
b
e
0.2 0.8
0.01 0.99
0.9 0.1
be
b
b
e
BE P(A | B,E)Earthquake
JohnCalls
Alarm
MaryCalls
Burglary
...
+ P(j|a) * P(m|a) * P(a|e,b) * P(e) * P(b)
burglary.
earthquake.
alarm :- burglary, earthquake.
marycalls :- alarm.
johncalls :- alarm.
Bayesian Networks [Pearl 91]
Expressiveness Bayesian Nets
A Bayesian net defines a probability distribution over a propositional logic
Essentially, the possible states (worlds) are propositional interpretations
But propositional logic is severely limited in expressive power, therefore consider combining BNs with logic programs• Bayesian logic programs• Actually, a BLP + some background knowledge
generates a BN• So, BLP is a kind of BN template !!!
0.9 0.1e
b
e0.2 0.8
0.01 0.990.9 0.1
be
b
b
e
BE P(A | B,E)Earthquake
JohnCalls
Alarm
MaryCalls
Burglary
Bayesian Logic Programs (BLPs)
alarm/0
earthquake/0 burglary/0
maryCalls/0 johnCalls/0
alarm
earthquake burglary
0.9 0.1e
b
e0.2 0.8
0.01 0.990.9 0.1
be
b
b
e
BE P(A | B,E)
local BN fragment
Rule Graph
alarm :- earthquake, burglary.
[Kersting, De Raedt]
bt
pc mc
Person
ba(0.0,0.0,1.0,0.0)
.........
aa(1.0,0.0,0.0,0.0)
mc(Person)pc(Person)bt(Person)
Bayesian Logic Programs (BLPs)
bt/1
pc/1 mc/1
argument
predicate
atombt(Person) :- pc(Person),mc(Person).
variable
Rule Graph
mc
pc mc
Person
mother
ba(0.5,0.5,0.0)
.........
aa(1.0,0.0,0.0)
mc(Mother)pc(Mother)mc(Person)
Mother
[Kersting, De Raedt]
Bayesian Logic Programs (BLPs)
bt/1
pc/1 mc/1
pc(Person) | father(Father,Person), pc(Father),mc(Father).
mc(Person) | mother(Mother,Person), pc(Mother),mc(Mother).
bt(Person) | pc(Person),mc(Person).
mc
pc mc
Person
mother
ba(0.5,0.5,0.0)
.........
aa(1.0,0.0,0.0)
mc(Mother)pc(Mother)mc(Person)
Mother
[Kersting, De Raedt]
Bayesian Logic Programs (BLPs)
father(rex,fred). mother(ann,fred).
father(brian,doro). mother(utta, doro).
father(fred,henry). mother(doro,henry).
mc(rex)
bt(rex)
pc(rex)mc(ann) pc(ann)
bt(ann)
mc(fred) pc(fred)
bt(fred)
mc(brian)
bt(brian)
pc(brian)mc(utta) pc(utta)
bt(utta)
mc(doro) pc(doro)
bt(doro)
mc(henry)pc(henry)
bt(henry)
pc(Person) | father(Father,Person), pc(Father),mc(Father).
mc(Person) | mother(Mother,Person), pc(Mother),mc(Mother).
bt(Person) | pc(Person),mc(Person).
Bayesian Network induced over least Herbrand model
Bayesian logic programs
Computing the ground BN (the BN that defines the semantics)• Compute the least Herbrand Model of the BLP • For each clause H | B1, … BN with CPD
if there is a substitution such that {H , B1 , …,BN } subset LHM, then H ’s parents include B1 , …,BN , and with CPD specified by the clause
• Delete logical atoms from BN (as their truth-value is known) - e.g. mother, father in the example
• Possibly apply aggregation and combining rules For specific queries, only part of the resulting BN
is necessary, the support net, cf. Next slides
Procedural Semantics
mc(rex)
bt(rex)
pc(rex)mc(ann) pc(ann)
bt(ann)
mc(fred) pc(fred)
bt(fred)
mc(brian)
bt(brian)
pc(brian)mc(utta) pc(utta)
bt(utta)
mc(doro) pc(doro)
bt(doro)
mc(henry)pc(henry)
bt(henry)
P(bt(ann)) ?
Procedural Semantics
mc(rex)
bt(rex)
pc(rex)mc(ann) pc(ann)
bt(ann)
mc(fred) pc(fred)
bt(fred)
mc(brian)
bt(brian)
pc(brian)mc(utta) pc(utta)
bt(utta)
mc(doro) pc(doro)
bt(doro)
mc(henry)pc(henry)
bt(henry)
P(bt(ann), bt(fred)) ?
P(bt(ann)| bt(fred)) =
P(bt(ann),bt(fred))
P(bt(fred))
Bayes‘ rule
Combining Rules
P(A|B,C)
P(A|B) and P(A|C)
CR
Any algorithm which has an empty output if and only if the input is empty combines a set of CPDs into a single (combined) CPD
E.g. noisy-or
prepared(Student,Topic) | read(Student,Book),
discusses(Book,Topic).
prepared
Studentread
discussesBook
Topic
Combining Partial Knowledge
prepared(s1,bn)
discusses(b1,bn)
prepared(s2,bn)
discusses(b2,bn)
variable # of parents for prepared/2 due to read/2• whether a student prepared a topic depends
on the books she read
CPD only for one book-topic pair
prepared(Student,Topic) | read(Student,Book),
discusses(Book,Topic).
prepared
Studentread
discussesBook
Topic
Summary BLPs
bt
pc mc
Person
bt
pc mc
Person
mc
pc mc
Person
mother
Mother
mc
pc mc
Person
mother
Mother
pc
pc mc
Person
father
Father
pc
pc mc
Person
father
Father
bt/1
pc/1 mc/1
bt/1
pc/1 mc/1
pc(Person) | father(Father,Person), pc(Father),mc(Father).mc(Person) | mother(Mother,Person), pc(Mother),mc(Mother).
bt(Person) | pc(Person),mc(Person).
Underlying logic pogram
+ (macro) CPDs
=Joint probability distribution over the least
Herbrand interpretation
+ CRs
+ Consequence operator
ba(0.5,0.5,0.0)
.........
aa(1.0,0.0,0.0)
mc(Mother)pc(Mother)mc(Person)
noisy-or, ...
If the body holds then the head holds, too.
mc(rex)
bt(rex)
pc(rex)mc(ann) pc(ann)
bt(ann)
mc(fred) pc(fred)
bt(fred)
mc(brian)
bt(brian)
pc(brian)mc(utta ) pc(utta)
bt(utta)
mc(doro) pc(doro)
bt(doro)
mc(henry)pc(henry)
bt(henry)
mc(rex)
bt(rex)
pc(rex)mc(ann) pc(ann)
bt(ann)
mc(fred) pc(fred)
bt(fred)
mc(brian)
bt(brian)
pc(brian)mc(utta ) pc(utta)
bt(utta)
mc(doro) pc(doro)
bt(doro)
mc(henry)pc(henry)
bt(henry)
=Conditional independencies
encoded in the induced BN
structure
Local
probability
models
Bayesian Logic Programs- Examples
% apriori nodesnat(0).
% aposteriori nodesnat(s(X)) | nat(X).
nat(0) nat(s(0)) nat(s(s(0)) ...MC
% apriori nodesstate(0).
% aposteriori nodesstate(s(Time)) | state(Time).output(Time) | state(Time)
state(0)
output(0)
state(s(0))
output(s(0))
...HMM
% apriori nodesn1(0).
% aposteriori nodesn1(s(TimeSlice) | n2(TimeSlice).n2(TimeSlice) | n1(TimeSlice).n3(TimeSlice) | n1(TimeSlice), n2(TimeSlice).
n1(0)
n2(0)
n3(0)
n1(s(0))
n2(s(0))
n3(s(0))
...DBN
pure P
rolo
g
Learning BLPs from Interpretations
Model(1)
earthquake=yes,
burglary=no,
alarm=?,
marycalls=yes,
johncalls=no
Model(1)
earthquake=yes,
burglary=no,
alarm=?,
marycalls=yes,
johncalls=no
Earthquake
JohnCalls
Alarm
MaryCalls
Burglary
Model(2)
earthquake=no,
burglary=no,
alarm=no,
marycalls=no,
johncalls=no
Model(2)
earthquake=no,
burglary=no,
alarm=no,
marycalls=no,
johncalls=no
Model(3)
earthquake=?,
burglary=?,
alarm=yes,
marycalls=yes,
johncalls=yes
Model(3)
earthquake=?,
burglary=?,
alarm=yes,
marycalls=yes,
johncalls=yes
Data case: • Random Variable + States = (partial) Herbrand interpretation
Model(1)
pc(brian)=b,
bt(ann)=a,
bt(brian)=?,
bt(dorothy)=a
Model(1)
pc(brian)=b,
bt(ann)=a,
bt(brian)=?,
bt(dorothy)=a
Model(2)
bt(cecily)=ab,
pc(henry)=a,
mc(fred)=?,
bt(kim)=a,
pc(bob)=b
Model(2)
bt(cecily)=ab,
pc(henry)=a,
mc(fred)=?,
bt(kim)=a,
pc(bob)=b
Background
m(ann,dorothy),
f(brian,dorothy),
m(cecily,fred),
f(henry,fred),
f(fred,bob),
m(kim,bob),
...
Background
m(ann,dorothy),
f(brian,dorothy),
m(cecily,fred),
f(henry,fred),
f(fred,bob),
m(kim,bob),
...
Model(3)
pc(rex)=b,
bt(doro)=a,
bt(brian)=?
Model(3)
pc(rex)=b,
bt(doro)=a,
bt(brian)=?
Bloodtype example
Learning BLPs from Interpretations
Parameter Estimation - BLPs
bt
pc mc
Person
bt
pc mc
Person
mc
pc mc
Person
mother
Mother
mc
pc mc
Person
mother
Mother
pc
pc mc
Person
father
Father
pc
pc mc
Person
father
Father
bt/1
pc/1 mc/1
bt/1
pc/1 mc/1
ba(0.5,0.5,0.0)
.........
aa(1.0,0.0,0.0)
mc(Mother)pc(Mother)mc(Person)
ba(0.5,0.5,0.0)
.........
aa(1.0,0.0,0.0)
mc(Mother)pc(Mother)mc(Person)
Database
D
+bt
pc mc
Person
bt
pc mc
Person
mc
pc mc
Person
mother
Mother
mc
pc mc
Person
mother
Mother
pc
pc mc
Person
father
Father
pc
pc mc
Person
father
Father
bt/1
pc/1 mc/1
bt/1
pc/1 mc/1
Underlying
Logic program
L
Learning
Algorithm
Parameter
Parameter Estimation – BLPs Estimate the CPD entries that best fit the data
„Best fit“: ML parameters
argmaxP( data | logic program,
argmaxlog P( data | logic program,
Reduces to problem to estimate parameters of a Bayesian networks:
given structure,
partially observed random variables
Parameter Estimation – BLPs
bt
pc mc
Person
bt
pc mc
Person
mc
pc mc
Person
mother
Mother
mc
pc mc
Person
mother
Mother
pc
pc mc
Person
father
Father
pc
pc mc
Person
father
Father
bt/1
pc/1 mc/1
bt/1
pc/1 mc/1
Model(1)
pc(brian)=b,
bt(ann)=a,
bt(brian)=?,
bt(dorothy)=a
Model(1)
pc(brian)=b,
bt(ann)=a,
bt(brian)=?,
bt(dorothy)=a
Background
m(ann,dorothy),
f(brian,dorothy),
m(cecily,fred),
f(henry,fred),
f(fred,bob),
m(kim,bob),
...
Background
m(ann,dorothy),
f(brian,dorothy),
m(cecily,fred),
f(henry,fred),
f(fred,bob),
m(kim,bob),
...
Model(2)
bt(cecily)=ab,
bt(henry)=a,
bt(fred)=?,
bt(kim)=a,
bt(bob)=b
Model(2)
bt(cecily)=ab,
bt(henry)=a,
bt(fred)=?,
bt(kim)=a,
bt(bob)=b
Model(3)
pc(rex)=b,
bt(doro)=a,
bt(brian)=?
Model(3)
pc(rex)=b,
bt(doro)=a,
bt(brian)=?
+
Parameter Estimation – BLPs
bt
pc mc
Person
bt
pc mc
Person
mc
pc mc
Person
mother
Mother
mc
pc mc
Person
mother
Mother
pc
pc mc
Person
father
Father
pc
pc mc
Person
father
Father
bt/1
pc/1 mc/1
bt/1
pc/1 mc/1
Model(1)
pc(brian)=b,
bt(ann)=a,
bt(brian)=?,
bt(dorothy)=a
Model(1)
pc(brian)=b,
bt(ann)=a,
bt(brian)=?,
bt(dorothy)=a
Background
m(ann,dorothy),
f(brian,dorothy),
m(cecily,fred),
f(henry,fred),
f(fred,bob),
m(kim,bob),
...
Background
m(ann,dorothy),
f(brian,dorothy),
m(cecily,fred),
f(henry,fred),
f(fred,bob),
m(kim,bob),
...
Model(2)
bt(cecily)=ab,
bt(henry)=a,
bt(fred)=?,
bt(kim)=a,
bt(bob)=b
Model(2)
bt(cecily)=ab,
bt(henry)=a,
bt(fred)=?,
bt(kim)=a,
bt(bob)=b
Model(3)
pc(rex)=b,
bt(doro)=a,
bt(brian)=?
Model(3)
pc(rex)=b,
bt(doro)=a,
bt(brian)=?
+
Parameter tying
EM – BLPs
bt
pc mc
Person
bt
pc mc
Person
mc
pc mc
Person
mother
Mother
mc
pc mc
Person
mother
Mother
pc
pc mc
Person
father
Father
pc
pc mc
Person
father
Father
bt/1
pc/1 mc/1
bt/1
pc/1 mc/1
Initial Parameters 0
Logic Program L
Expected counts of a clause
Expectation
Inference
Update parameters (ML, MAP)
Maximization
EM-algorithm:iterate until convergence
Current Model(k)
Model(1)
pc(brian)=b,
bt(ann)=a,
bt(brian)=?,
bt(dorothy)=a
Model(1)
pc(brian)=b,
bt(ann)=a,
bt(brian)=?,
bt(dorothy)=a
Background
m(ann,dorothy),
f(brian,dorothy),
m(cecily,fred),
f(henry,fred),
f(fred,bob),
m(kim,bob),
...
Background
m(ann,dorothy),
f(brian,dorothy),
m(cecily,fred),
f(henry,fred),
f(fred,bob),
m(kim,bob),
...
Model(2)
bt(cecily)=ab,
bt(henry)=a,
bt(fred)=?,
bt(kim)=a,
bt(bob)=b
Model(2)
bt(cecily)=ab,
bt(henry)=a,
bt(fred)=?,
bt(kim)=a,
bt(bob)=b
Model(3)
pc(rex)=b,
bt(doro)=a,
bt(brian)=?
Model(3)
pc(rex)=b,
bt(doro)=a,
bt(brian)=?
P( head(GI), body(GI) | DC )MM
DataCase
DC
Ground InstanceGI
P( head(GI), body(GI) | DC )MM
DataCaseDC
Ground InstanceGI
P( body(GI) | DC )MM
DataCaseDC
Ground InstanceGI
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